Question

maximum value of
the given expression
and
the
corresponding value
of x, if x takes only
real values?
p(x) = 289 - (x - 17)​

Answer 1

Step-by-step explanation:

=289-(x-17)

=289-x+17

=306-x

so, x=306

Answer 2

The maximum value of the expression is 289 and the corresponding value of x=17.

Given:

p(x) = 289 - $(x-17)^{2}$

To Find:

The maximum value of the given expression and the corresponding value

of x.

Solution:

We will apply the second derivative test to solve this problem.

p'(x) = -2(x-17)

On equating p'(x) to zero, we get

p'(x) = 0 ⇒ x = 17

Taking the second derivative

p"(x) = -2 < 0

The above inequality is valid for x=17. Since the second derivative is less than 0 at x = 17, we obtain maximum value at x = 17.

The maximum value is p(17) = 289 - $(17-17)^{2}$ = 289

Hence the maximum value of the expression is 289 and the corresponding value of x=17.

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